This book offers a comprehensive and timely overview of the latest developments in the field of biomechanics and extensive knowledge of tissue structure, function, and modeling. Gathering chapters written by authoritative scientists, it reports on a range of continuum and computational models of solids, and related experimental works, for biomechanical applications. It discusses cutting-edge advances such as constitutive modeling and computational simulation of biological tissues and organs under physiological and pathological conditions, and their mechanical characterization. It covers  innovative studies on arteries, heart, valvular tissue, and thrombus, brain tumor, muscle, liver, kidney, and stomach, among others. Written in honor of Professor Gerhard A. Holzapfel,  the book provides specialized readers with a thorough and timely overview of different types of modeling in biomechanics, and current knowledge about biological structures and function.

As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben eficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a du ality gap between the two partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications which fall into the two following complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited vol umes and selected conference proceedings. The AMMA annual book publishes invited and contributed compre hensive reviews, research and survey articles within the broad area of modern mechanics and applied mathematics. Mechanics is understood here in the most general sense of the word, and is taken to embrace relevant physical and biological phenomena involving electromagnetic, thermal and quantum effects and biomechanics, as well as general dy namical systems. Especially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other fields. All contributions will be reviewed so as to guarantee the highest possible scientific standards."

Nonsmoothness and nonconvexity arise in numerous applications of mechan- ics and modeling due to the need for studying more and more complicated phe- nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap- plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical questions. Because of the upsurge in activity in the area of nonsmooth and noncon- vex mechanics, Professors Gao and Ogden, together with the late Professor P.D. Panagiotopoulos, had planned to organize a Minisymposium with the title Nonsmooth and Nonconvex Mechanics within the ASME 1999 Mechanics & Materials Conference, June 27-30 1999, Blacksburg, Virginia. After the unex- pected death of Professor Panagiotopoulos the first two editors invited the third editor (Professor Stavroulakis) to join them. A large number of mathematical and engineering colleagues supported our efforts by presenting lectures at the Minisymposium in which the available mathematical methods were described and many problems of nonsmooth and nonconvex mechanics were discussed. The interest of the many participants encourages us all to continue our research efforts.

Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.

As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben eficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a du ality gap between the two partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications which fall into the two following complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited vol umes and selected conference proceedings. The AMMA annual book publishes invited and contributed compre hensive reviews, research and survey articles within the broad area of modern mechanics and applied mathematics. Mechanics is understood here in the most general sense of the word, and is taken to embrace relevant physical and biological phenomena involving electromagnetic, thermal and quantum effects and biomechanics, as well as general dy namical systems. Especially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other fields. All contributions will be reviewed so as to guarantee the highest possible scientific standards."

Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the beneficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a duality gap between the two partners, and this gap is growing wider.
Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.
Audience: Scientists and mathematicians, including advanced students (doctoral and post-doctoral level) at universities and in industry interested in mechanics and applied mathematics.

Nonsmoothness and nonconvexity arise in numerous applications of mechan- ics and modeling due to the need for studying more and more complicated phe- nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap- plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical questions. Because of the upsurge in activity in the area of nonsmooth and noncon- vex mechanics, Professors Gao and Ogden, together with the late Professor P.D. Panagiotopoulos, had planned to organize a Minisymposium with the title Nonsmooth and Nonconvex Mechanics within the ASME 1999 Mechanics & Materials Conference, June 27-30 1999, Blacksburg, Virginia. After the unex- pected death of Professor Panagiotopoulos the first two editors invited the third editor (Professor Stavroulakis) to join them. A large number of mathematical and engineering colleagues supported our efforts by presenting lectures at the Minisymposium in which the available mathematical methods were described and many problems of nonsmooth and nonconvex mechanics were discussed. The interest of the many participants encourages us all to continue our research efforts.

This book offers a comprehensive and timely overview of the latest developments in the field of biomechanics and extensive knowledge of tissue structure, function, and modeling. Gathering chapters written by authoritative scientists, it reports on a range of continuum and computational models of solids, and related experimental works, for biomechanical applications. It discusses cutting-edge advances such as constitutive modeling and computational simulation of biological tissues and organs under physiological and pathological conditions, and their mechanical characterization. It covers innovative studies on arteries, heart, valvular tissue, and thrombus, brain tumor, muscle, liver, kidney, and stomach, among others. Written in honor of Professor Gerhard A. Holzapfel, the book provides specialized readers with a thorough and timely overview of different types of modeling in biomechanics, and current knowledge about biological structures and function.